Peres lattice and classical Peres invariant

Poincaré section y = 0 calculated on the 100 x 100 grid.
A trajectory is started at each point of the grid and the
SALI
method is used to distinguish regular (blue colour) from chaotic (red colour) trajectories.

Figure 3: Peres lattice of the operator L^2

Figure 4: Classical Peres invariant

3000 lowest lying well-converging states are displayed.
The grey line corresponds with the energy E=0, on which the section of regularity (Figure 2) and the Peres invariant (Figure 4)
are calculated.

Time averaged value of the variable L^2, calculated on the 400 x 400 grid.